The inductor/capacitor tank circuit (hereinafter “LC tank”) could be applied in various circuits, for example: a modulator, a Voltage Controlled Oscillator (VCO), etc. The central frequency (f) of an LC tank could be represented by the formula
  f  =            1              2        ⁢                                  ⁢        π        ⁢                  LC                      .  In order to overcome the central frequency offset from the ideal value of the design, adjustment of the capacitance (C) or the inductance (L) is required. Conventionally, there are three methods for adjusting the capacitance or inductance and they will be described as follows.
Please refer to FIG. 1A, which is a diagram of a conventional switching capacitor. Capacitors C1, C2 and C3 are connected in parallel and capacitors C2 and C3 are respectively connected in series with switches A10. It should be noted that although not required, switch A10 could be implemented with a MOS transistor. Capacitors C2 and C3 are loaded onto the LC tank when switch A10 is turned on, whereas capacitors C2 and C3 are unloaded from the LC tank when switch A10 is turned off. The shortcoming of this method is that switch A10 generates parasitic resistance. Since the Q factor (Q) of the LC tank could be derived with the formula
      Q    =                                        W            0                    ⁢          L                R            =              1                              RW            0                    ⁢          C                      ,where W0 is resonant frequency and R is resistance, the parasitic resistance generated in switch A10 would reduce the Q factor of the LC tank, which represents a reduction of circuit performance.
Please refer to FIG. 1B, which is a diagram of a conventional trimmable capacitor. Capacitors C1, C2 and C3 are connected in parallel, and capacitors C2 and C3 respectively are connected in series with trimmable wire A20. When reduction of capacitance is required (for increasing the central frequency of LC tank), trimmable wire A20 (which is serially coupled with either capacitor C2 or C3), is trimmed to unload capacitor C2 or C3 from the LC tank. The advantage of this method is that parasitic resistance is not generated, and the Q factor is not reduced thereby. However, this method works only when an increase of the central frequency is required.
Please refer to FIG. 1C, which is a diagram of a conventional switching inductor. Inductors L1 and L2 are connected with each other in series, and are in turn connected in parallel with capacitor C. Inductor L1 is also connected with switch A10 in parallel. It should be noted that although not required, switch A10 could be implemented with a field-effect transistor (FET). Inductor L1 is loaded onto the LC tank when switch A10 is turned off, and unloaded from the LC tank when switch A10 is turned on. The shortcoming of this method is that switch A10 will also generate parasitic resistance, which reduces the Q factor of the LC tank, and further reduces the circuit performance.
It may be seen from the preceding, therefore, that adjustment of the Q factor is an important issue.